Calculation of critical points using a reduction method

Efficient and accurate calculation of critical points is an important aspect of general phase equilibrium calculations. When calculating critical points, the computationally expensive part is to solve the spinodal equation. For Heidemann and Khalil formulation the dimensionality of the problem is equal to the number of components (nc). In this paper we describe a new procedure enabling the reduction of problem dimensionality.

The reduction is effectively achieved by spectral decomposition of the matrix with elements (1 − Cij), where Cij denotes the binary interaction parameters (BIP). The dimensionality of the problem is given by the number of reduction parameters, M = m + 1, where m is the number of nonzero (or non-negligible) eigenvalues of . The spinodal equation consists in equating to zero a determinant of order M (for naturally occurring hydrocarbon mixtures, M is much less than nc). The procedure suggested by Michelsen and Heidemann for zero BIP is a particular case of our approach.